Simplify 3/10x + 1/6y + 3/10x + 3/6y . Be sure to reduce any fractions to the lowest terms.

Answer 1

To simplify the expression \( \frac{3}{10}x + \frac{1}{6}y + \frac{3}{10}x + \frac{3}{6}y \), we can first combine like terms.

1. Combine the \( x \) terms: \[ \frac{3}{10}x + \frac{3}{10}x = \frac{6}{10}x \]

   Now simplify \( \frac{6}{10} \): \[ \frac{6}{10} = \frac{3}{5} \] So, \( \frac{6}{10}x = \frac{3}{5}x \).

2. Next, combine the \( y \) terms: \[ \frac{1}{6}y + \frac{3}{6}y = \frac{4}{6}y \]

   Now simplify \( \frac{4}{6} \): \[ \frac{4}{6} = \frac{2}{3} \] So, \( \frac{4}{6}y = \frac{2}{3}y \).

3. Now, put the simplified terms together: \[ \frac{3}{5}x + \frac{2}{3}y \]

Thus, the simplified expression is: \[ \frac{3}{5}x + \frac{2}{3}y \]